Mixtures of like-charged colloids and flexible polymers in solution are studied at the statistical mechanics of liquids level. The spatial correlations between monomers inside the semi-dilute polyelectrolyte are investigated using the polymer reference interaction site model. In the bare Debye-Huckel picture, charged sites (colloids and monomers) interact via ion-averaged, screened coulombic potentials. The network of the entangled charged chains exert a depletion attraction of entropic and electrostatic origins onto title colloidal particles, which leads to a phase separation of the solution between colloid-rich and polymer-rich phases. The presence of hydrophobic sites on partly charged polymer chains (sequential copolymers) alters this picture and induces steric repulsion and bridging attraction between colloids.